Report 23: tracking of COVID-19 in the United States …...2020/05/21 · Caroline Walters, Yuanrong Wang, Oliver J Watson, Lilith Whittles, Azra Ghani, Neil M Ferguson, Steven Riley,

21 May 2020 Imperial College COVID-19 Response Team

DOI: https://doi.org/10.25561/79231 Page 1

Report 23: State-level tracking of COVID-19 in the United States

H Juliette T Unwin∗, Swapnil Mishra∗2, Valerie C Bradley∗, Axel Gandy∗, Michaela Vollmer, Thomas Mellan, Helen Coup-

land, Kylie Ainslie, Charlie Whittaker, Jonathan Ish-Horowicz, Sarah Filippi, Xiaoyue Xi, Melodie Monod, Oliver Ratmann,

Michael Hutchinson, Fabian Valka, Harrison Zhu, Iwona Hawryluk, Philip Milton, Marc Baguelin, Adhiratha Boonyasiri,

Nick Brazeau, Lorenzo Cattarino, Giovanni Charles, Laura V Cooper, Zulma Cucunuba, Gina Cuomo-Dannenburg, Bimandra

Djaafara, Ilaria Dorigatti, Oliver J Eales, Jeff Eaton, Sabine van Elsland, Richard FitzJohn, Katy Gaythorpe, William Green,

Timothy Hallett, Wes Hinsley, Natsuko Imai, Ben Jeffrey, Edward Knock, Daniel Laydon, John Lees, Gemma Nedjati-Gilani,

Pierre Nouvellet, Lucy Okell, Alison Ower, Kris V Parag, Igor Siveroni, Hayley A Thompson, Robert Verity, Patrick Walker,

Caroline Walters, Yuanrong Wang, Oliver J Watson, Lilith Whittles, Azra Ghani, Neil M Ferguson, Steven Riley, Christl A.

Donnelly, Samir Bhatt1,∗ and Seth Flaxman∗

Department of Infectious Disease Epidemiology, Imperial College London

Department of Mathematics, Imperial College London

WHO Collaborating Centre for Infectious Disease Modelling

MRC Centre for Global Infectious Disease Analytics

Abdul Latif Jameel Institute for Disease and Emergency Analytics, Imperial College London

Department of Statistics, University of Oxford

*Contributed equially1Correspondence: [email protected] correspondence: [email protected]

SUGGESTED CITATIONH Juliette Unwin, Swapnil Mishra, Valerie C Bradley et al. State-level tracking of COVID-19 in the United States (21-05-2020), doi: https://doi.org/10.25561/79231.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

https://doi.org/10.25561/79231

https://creativecommons.org/licenses/by-nc-nd/4.0/


Summary

As of 20 May 2020, the US Centers for Disease Control and Prevention reported 91,664 confirmed or probable COVID-

19-related deaths, more than twice the number of deaths reported in the next most severely impacted country. In

order to control the spread of the epidemic and prevent health care systems from being overwhelmed, US states have

implemented a suite of non-pharmaceutical interventions (NPIs), including “stay-at-home” orders, bans on gatherings,

and business and school closures.

We model the epidemics in the US at the state-level, using publicly available death data within a Bayesian hierarchical

semi-mechanistic framework. For each state, we estimate the time-varying reproduction number (the average number of

secondary infections caused by an infected person), the number of individuals that have been infected and the number

of individuals that are currently infectious. We use changes in mobility as a proxy for the impact that NPIs and other

behaviour changes have on the rate of transmission of SARS-CoV-2. We project the impact of future increases in mobility,

assuming that the relationship between mobility and disease transmission remains constant. We do not address the

potential effect of additional behavioural changes or interventions, such as increasedmask-wearing or testing and tracing

strategies.

Nationally, our estimates show that the percentage of individuals that have been infected is 4.1% [3.7%-4.5%], with wide

variation between states. For all states, even for the worst affected states, we estimate that less than a quarter of the

population has been infected; in New York, for example, we estimate that 16.6% [12.8%-21.6%] of individuals have been

infected to date. Our attack rates for NewYork are in linewith those from recent serological studies [1] broadly supporting

our modelling choices.

There is variation in the initial reproduction number, which is likely due to a range of factors; we find a strong association

between the initial reproduction numberwith both population density (measured at the state level) and the chronological

date when 10 cumulative deaths occurred (a crude estimate of the date of locally sustained transmission).

Our estimates suggest that the epidemic is not under control in much of the US: as of 17 May 2020, the reproduction

number is above the critical threshold (1.0) in 24 [95% CI: 20-30] states. Higher reproduction numbers are geographically

clustered in the South andMidwest, where epidemics are still developing, whilewe estimate lower reproduction numbers

in states that have already suffered high COVID-19mortality (such as theNortheast). These estimates suggest that caution

must be taken in loosening current restrictions if effective additional measures are not put in place.

We predict that increased mobility following relaxation of social distancing will lead to resurgence of transmission, keep-

ing all else constant. We predict that deaths over the next two-month period could exceed current cumulative deaths

by greater than two-fold, if the relationship between mobility and transmission remains unchanged. Our results suggest

that factors modulating transmission such as rapid testing, contact tracing and behavioural precautions are crucial to

offset the rise of transmission associated with loosening of social distancing.

Overall, we show that while all US states have substantially reduced their reproduction numbers, we find no evidence

that any state is approaching herd immunity or that its epidemic is close to over.

We invite scientific peer reviews here: https://openreview.net/group?id=-Agora/COVID-19


https://openreview.net/group?id=-Agora/COVID-19

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1 Introduction

The first death caused by COVID-19 in the United States is currently believed to have occurred in Santa Clara, California on

the 6th February [2]. In April 2020, the number of deaths attributed to COVID-19 in the United States (US) surpassed that

of Italy [3]. Throughout March 2020, US state governments implemented a variety of non-pharmaceutical interventions

(NPIs), such as school closures and stay-at-home orders, to limit the spread of SARS-CoV-2 and help maintain the capacity

of health systems to treat as many severe cases of COVID-19 as possible. Courtemanche et al. [4] use an event-study

model to determine that such NPIs were successful in reducing the growth rate of COVID-19 cases across US counties.

We similarly seek to estimate the impact of NPIs on COVID-19 transmission, but do so with a semi-mechanistic Bayesian

model that reflects the underlying process of disease transmission and relies on mobility data released by companies

such as Google [5]. Mobility measures reveal stark changes in behaviour following large-scale government interventions,

with individuals spending more time at home and correspondingly less time at work, at leisure centres, shopping, and

on public transit. Some state governments, like the Colorado Department of Public Health, have already begun to use

similar mobility data to adjust guidelines over social distancing [6]. As more and more states ease the stringency of

their NPIs, future policy decisions will rely on the interaction between mobility and NPIs and their subsequent impact on

transmission.

In a previous report [7], we introduced a new Bayesian statistical framework for estimating the rate of transmission and

attack rates for COVID-19. Our approach infers the time-varying reproduction number,Rt, which measures transmission

intensity. We calculate the number of new infections through combining previous infections with the generation interval

(the distribution of times between infections). The number of deaths is then a function of the number of infections

and the infection fatality rate (IFR). We estimate the posterior probability of our parameters given the observed data,

while incorporating prior uncertainty. This makes our approach empirically driven while incorporating as many sources

of uncertainty as possible. In this report, similar to [8, 9], we adapt our original framework to model transmission in the

US at the state level. In our formulationwe parameteriseRt as a function of several mobility types. Our parameterisation

ofRt makes the explicit assumption that changes in transmission are reflected throughmobility. While we do attempt to

account for residual variation, we note that transmissionwill also be influence by additional factors and some of these are

confounded causally with mobility. We utilise partial pooling of parameters, where information is shared across all states

to leverage asmuch signal as possible, but individual effects are also included for state- and region-specific idiosyncrasies.

Our partial pooling model requires only one state to provide a signal for the impact of mobility, and then this effect is

shared across all states. While this sharing can potentially lead to initial over or under estimation effect sizes, it also

means that a consistent signal for all states can be estimated before that signal is presented in an individual states with

little data.

We infer plausible upper and lower bounds (Bayesian credible interval summaries of our posterior distribution) of the

total population that have been infected by COVID-19 (also called the cumulative attack rate or attack rate). We also

estimate the effective number of individuals currently infectious given our generation distribution. We investigate how

the reproduction number has changed over time and study the heterogeneity in starting and ending rates by state, date,

and population density. We assess whether there is evidence that changes in mobility have so far been successful at

reducing Rt to less than 1. To assess the risk of resurgence when interventions are eased, we use simple scenarios of

increased mobility and simulate forwards in time. From these simulations we study how sensitive individual states are


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to resurgence, and the plausible magnitude of this resurgence.

Details of the data sources and a technical description of our model and are found in Sections 4 and 5 respectively.

General limitations of our approach are presented below in the conclusions.

2 Results

2.1 Mobility trends, interventions and effect sizes

Mobility data provide a proxy for the behavioural changes that occur in response to non-pharmaceutical interventions.

Figure 1 shows trends in mobility for the 50 states and the District of Columbia (see Section 4 for a description of the

mobility dimensions). Regions are based on US Census Divisions, modified to account for coordination between groups

of state governments [10]. These trends are relative to a state-dependent baseline, which was calculated shortly before

the COVID-19 epidemic. For example, a value of −20% in the transit station trend means that individuals, on average,

are visiting and spending 20% less time in transit hubs than before the epidemic. In Figure 1, we overlay the timing of

two major state-wide NPIs (stay at home and emergency decree) (see [11] for details). We also note intuitive changes in

mobility such as the spike on 11th and 12th April for Easter. In our model, we use the time spent at one’s residence and

the average of time spent at grocery stores, pharmacies, recreation centres, andworkplaces. For states in which the 2018

American Community Survey reports that more than 20% of the working population commutes on public transportation,

we also use the time spent at transit hubs (including gas stations etc.) [12].

To justify the use of mobility as a proxy for behaviour, we regress average mobility against the timings of major NPIs

(represented as step functions). The median correlation between the observed average mobility and the linear predic-

tions from NPIs was approximately 89% (see Appendix A). We observed reduced correlation when lagging (forward and

backwards) the timing of NPIs suggesting immediate impact on mobility. We make no explicit causal link between NPIs

and mobility, however, this relationship is plausibly causally linked but is confounded by other factors.

The mobility trends data suggests that the United States’ national focus on the New York epidemic may have led to

substantial changes in mobility in nearby states, like Connecticut, prior to any mandated interventions in those states.

This observation adds support to the hypothesis that mobility can act as a suitable proxy for the changes in behaviour

induced by the implementation of themajor NPIs. In further corroboration, a poll conducted byMorning Consult/Politico

on 26thMarch 2020 found that 81% of respondents agreed that “Americans should continue to social distance for as long

as is needed to curb the spread of coronavirus, even if it means continued damage to the economy” [13]. While support

for strong social distancing has since eroded slightly (70% agree in the same poll conducted later on 10 May 2020), the

overall high support for social distancing suggests strong compliance with NPIs, and that the changes to mobility that

we observe over the same time period are driven by adherence to those policy recommendations. However, we note

that mobility alone cannot capture all the heterogeneity in transmission risk. In particular, it cannot capture the impact

of case-based interventions (such as testing and tracing). To account for this residual variation missed by mobility we

use a second-order, weekly, autoregressive process. This autoregressive process is an additional term in our parametric

equation forRt and accounts for residual noise by capturing a correlation structure where currentRt is correlated with

previous weeksRt (see Figures 12).


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Figure 2 shows the average global effect sizes for the mobility types used in our model. Estimates for the regional and

state-level effect sizes are included in Appendix B. We find that increased time spent in residences reduces transmission

by 54.3% [17.8% - 80.8%], and that decreases in overall averagemobility reduced transmission by 62.7% [43.1% - 74.5%].

These two effects are likely related - as people spend less time in public spaces, captured by our average mobility metric,

they conversely spendmore time at home. Overall, this decreases the number of people with whom the average individ-

ual comes into contact, thus slowing transmission, even if more time at home may increase transmission within a single

residence. We find time spent in transit hubs does not have a significant effect on transmission. The impact of transit

mobility is in contrast to what we observed in Italy [8], and likely reflects higher reliance on cars and less use of public

transit in the US than Europe [14].

The learnt random effects from the autoregressive process are shown in Appendix C. These results show that mobility

explains most of the changes in transmission in places without advanced epidemics, as evidenced by the flat residual

variation. However, for regions with advanced epidemics, such as New York or New Jersey, there is evidence of additional

decreases in transmission that cannot be explained by mobility alone. These may capture the impact of other control

measures, such as increased testing, as well as behavioural responses not captured by mobility, like increased mask-

wearing and hand-washing.

2.2 Impact of interventions on reproduction numbers

We estimate a national average initial reproduction number (Rt=0) of 2.2 [0.3 Montana - 5.0 New York] and find that,

similar to influenza transmission in cities (see Dalziel et al. [15]), Rt=0 is correlated with population density (Figure 3)1.

Dalziel et al. hypothesize that more personal contact occurs in more densely populated areas, thus resulting in a larger

Rt=0.

Rt=0 is also negatively correlated with when a state observed cumulative 10 deaths (Figure 3). This negative correlation

implies that states began locally sustained transmission later had a lowerRt=0. A possible hypothesis for this effect is the

onset of behavioural changes in response to other epidemics in the US. An alternative explanation is that the estimates of

the early growth rates of the epidemics in the states affected earliest are biased upwards by the early national ramp-up

of surveillance and testing. Despite Rt=0 being highly variable, in part due to the factors discussed above, the majority

of states have generally decreased theirRt since the first 10 deaths were observed (Figure 4). We estimate that 26 states

have a posterior mean Rt of less than one but only 8 have 95% credible intervals that are completely below one. A

posterior meanRt below one and credible interval that includes one suggests that the epidemic is likely under control in

that state, but the potential for increasing transmission cannot be ruled out. Therefore, our results show that very few

states have conclusively controlled their epidemics. Of the ten states with the highest current Rt, half are in the Great

Lakes region (Illinois, Ohio, Minnesota Indiana, and Wisconsin). In Figure 5 we show the geographical variation in the

posterior probability that Rt is less than 1; green states are those with probability that Rt is below 1 is high, and pink

states are those with low probability. The closer a value is to 100%, the more certain we are that the rate of transmission

is below 1 and that new infections are not increasing at present. This is in contrast to many European countries that have

conclusively reduced theirRt less than one at present [7].

1We also considered the relationship of Rt with a population density weighted by proportion of the total population of the state in each census

tract. This was less strongly correlated toRt=0.


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Figure 1: Comparison of mobility data from Google with government interventions for the 50 states and the District of

Columbia. The solid lines show average mobility (across categories “retail & recreation”, “grocery & pharmacy”, “work-

places”), the dashed lines show “transit stations” and the dotted lines show “residential”. Intervention dates are indicated

by shapes as shown in the legend; see Section 4 for more information about the interventions implemented. There is a

strong correlation between the onset of interventions and reductions in mobility.


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●

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Transit

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0%(no effect on transmissibility)

25% 50% 75% 100%(ends transmissibility)

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Figure 2: Covariate effect sizes: Average mobility combines “retail & recreation”, “grocery & pharmacy”, “workplaces”.

Transit stations is only used as a covariate for states in which more than 20% of the working population commutes using

public transportation. We plot estimates of the posterior mean effect sizes and 95% credible intervals for each mobility

category. The relative % reduction in Rt metric is interpreted as follows: the larger the percentage, the more Rt de-

creases, meaning the disease spreads less; a 100% relative reduction ends disease transmissibility entirely. The smaller

the percentage, the less effect the covariate has on transmissibility. A 0% relative reduction has no effect onRt and thus

no effect on the transmissibility of the disease, while a negative percent reduction implies an increase in transmissibility.

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Figure 3: Comparison of initialRt=0 with population density (a) and date of 10 cumulative deaths (b). R-squared values

are 0.466 and 0.449 respectively.


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Figure 4: State-level estimates of initialRt and the current averageRt over the past week. The colours indicate regional

grouping as shown in Figure 1

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Figure 5 shows that while we are confident that some states have controlled transmission, we are similarly confident that

many states have not. Specifically, we are more than 50% sure thatRt > 1 in 25 states. There is substantial geographical

clustering; most states in the Midwest and the South have rates of transmission that suggest the epidemic is not yet

under control. We do note here that many states with Rt < 1 are still in the early epidemic phase with few deaths so

far.

2.3 Trends in COVID-19 transmission

In this section we focus on five states: Washington, New York, Massachusetts, Florida, and California. These states

represent a variety of COVID-19 government responses and outbreaks that have dominated the national discussion of


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0%

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Figure 5: Our estimates of the probability thatRt is less than one (epidemic control) for each state.

COVID-19. Figure 62 shows the trends for these states (trends for all other states can be found in appendix D). Regressing

average mobility against the timing of NPIs yielded an average correlation of around∼ 97%. Along with the strong visual

correspondence, these results suggest that that interventions have had a very strong effect on mobility, which given our

modelling assumptions, translates into effects on transmission intensity. We also note that there are clear day-of-the-

week fluctuations from the mobility data that affect transmission; these fluctuations are small compared to the overall

reductions in mobility.

On February 29th 2020, Washington state announced the nation’s first COVID-related death and became the first state to

declare a state of emergency. Despite observing its first COVID-19 death only a day after Washington state, New York did

not declare a state of emergency until 7 March 2020. We estimate that Rt began to decline in Washington state before

it did in New York, likely due to earlier intervention, but that stay-at-home orders in both states successfully reduced Rt

to less than one. However, we estimate thatRt in Washington has increased in recent weeks and is currently above one,

while it remains below one in New York (New York - 0.7 [0.4-1.1] and Washington - 0.9 [0.6-1.3]). Approximately one

week after New York, Massachusetts issued a stay-at-home order but the meanRt remains about one (1.1 [0.7-1.4]). In

Florida,Rt reduced noticeably before the stay-at-home order, suggesting that behaviour change started before the stay-

at-home order. However, increasing in mobility appears to have driven transmission up recently (1.2 [0.8-1.6]). California

implemented early interventions in San Francisco [16], and was the first state to issue a stay-at-home order [17], but the

meanRt still remains greater than one (1.0 [0.7-1.4]). For all the five states shown here there is considerable uncertainty

around the current value ofRt.

2.4 Attack rates

We show the percentage of total population infected, or cumulative attack rate, in Table 1 for all 50 states and the

District of Columbia. In general, the attack rates across states remain low; we estimate that the average percentage

of people that have been infected by COVID-19 is 4.1% [3.7%-4.5%]. However, this low national average masks a stark

2Death data until 17 May 2020 is included in our model and displayed in the plots; infections andRt are displayed consistent with the availability

of Google mobility data, until 9th May 2020.


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95%

Figure 6: State-level estimates of infections, deaths, and Rt for Washington, New York, Massachusetts, Florida, and

California. Left: daily number of deaths, brown bars are reported deaths, blue bands are predicted deaths, dark blue

50% credible interval (CI), light blue 95% CI. Middle: daily number of infections, brown bars are reported confirmed

cases, blue bands are predicted infections, CIs are same as left. Afterwards, if theRt is above 1, the number of infections

will start growing again. Right: time-varying reproduction number Rt dark green 50% CI, light green 95% CI. Icons are

interventions shown at the time they occurred.


https://doi.org/10.25561/79231


Table 1: Posterior model estimates of percentage of total population infected as of 17 May 2020.

State % of total population

infected (mean [95%

credible interval])

State % of total population

infected (mean [95%

credible interval])

Alabama 1.9% [1.2%-3.0%] Montana 0.2% [0.0%-0.4%]

Alaska 0.2% [0.0%-0.7%] Nebraska 1.2% [0.7%-2.0%]

Arizona 2.3% [1.4%-4.0%] Nevada 1.8% [1.3%-2.7%]

Arkansas 0.5% [0.3%-0.8%] New Hampshire 2.2% [1.3%-3.6%]

California 1.6% [1.1%-2.5%] New Jersey 16.1% [11.9%-21.7%]

Colorado 4.6% [3.1%-7.3%] New Mexico 2.6% [1.6%-4.3%]

Connecticut 13.3% [9.7%-18.3%] New York 16.6% [12.8%-21.6%]

Delaware 5.4% [3.5%-8.7%] North Carolina 1.1% [0.7%-1.7%]

District of Columbia 10.8% [7.6%-15.4%] North Dakota 0.9% [0.5%-1.6%]

Florida 1.3% [0.9%-2.0%] Ohio 2.6% [1.7%-4.0%]

Georgia 2.7% [1.9%-3.8%] Oklahoma 1.0% [0.7%-1.4%]

Hawaii 0.1% [0.0%-0.3%] Oregon 0.4% [0.2%-0.6%]

Idaho 0.6% [0.3%-0.8%] Pennsylvania 5.5% [3.7%-8.6%]

Illinois 7.1% [4.5%-11.2%] Rhode Island 6.8% [4.8%-9.9%]

Indiana 5.0% [3.2%-7.9%] South Carolina 1.2% [0.8%-1.8%]

Iowa 2.5% [1.5%-4.3%] South Dakota 1.0% [0.5%-1.9%]

Kansas 0.9% [0.6%-1.3%] Tennessee 0.7% [0.5%-1.2%]

Kentucky 1.0% [0.7%-1.4%] Texas 1.4% [0.8%-2.4%]

Louisiana 8.0% [6.0%-11.0%] Utah 0.5% [0.3%-0.9%]

Maine 0.5% [0.3%-0.8%] Vermont 0.8% [0.5%-1.3%]

Maryland 5.6% [3.9%-8.3%] Virginia 2.2% [1.4%-3.4%]

Massachusetts 13.0% [9.3%-18.3%] Washington 1.9% [1.4%-2.7%]

Michigan 5.9% [4.5%-7.8%] West Virginia 0.5% [0.3%-0.7%]

Minnesota 3.1% [1.8%-5.2%] Wisconsin 1.2% [0.8%-1.8%]

Mississippi 3.8% [2.4%-6.1%] Wyoming 0.3% [0.1%-0.6%]

Missouri 1.7% [1.1%-2.7%] National 4.1% [3.7%-4.5%]


https://doi.org/10.25561/79231


heterogeneity across states. New York and New Jersey have the highest estimated attack rates, of 16.6% [12.8%-21.6%]

and 16.1% [11.9%-21.7%] respectively, and Connecticut, Massachusetts, and Washington, D.C. all have attack rates over

10%. Conversely, other states that have drawn attention for early outbreaks, such as California, Washington, and Florida,

have attack rates of around 1%, and other states where the epidemic is still early, like Maine, having estimated attack

rates of less than 1%. We note here that there is the possibility of under reporting of deaths in these states. Under

reporting of COVID-19 attributable deaths will result in an underestimate of the attack rates. We note here that we have

found our estimates to be reasonably robust in settings where there is significant under reporting (e.g. Brazil [9]).

Figure 7 shows the effective number of infectious individuals and the number of newly infected individuals on any given

day for each of the 8 regions in ourmodel. The effective number of infectious individuals is calculated using the generation

time distribution, where individuals are weighted by how infectious they are over time. The fully infectious average

includes asymptotic and symptomatic individuals. Currently, we estimate that there are 1344000 [368000 - 3320000]

infectious individuals across the whole of the US, which corresponds to 0.42% [0.11% - 1.03%] of the population. Table

2 shows the number currently infected across different states is highly heterogeneous. Figure 7 shows that despite

new infections being in a steep decline, the number of people still infectious, and therefore able to sustain onward

transmission, can still be large. This discrepancy underscores the importance of testing and case based isolation as a

means to control transmission. We note that the expanding cone of uncertainty is in part due to uncertainties arising

from the lag between infections and deaths, but also from trends in mobility. State level estimates of the total number

of infectious individuals over time are given in Appendix E and the current number of infectious individuals are given in

Figure 2.

2.5 Scenarios

The relationship between mobility and transmission is the principle mechanism affecting values of Rt in our model.

Therefore, we illustrate the impact of likely near-term scenarios for Rt over the next 8 weeks, under assumptions of

relaxations of interventions leading to increased mobility. We note that mobility is acting here as a proxy for the number

of potentially infectious contacts. Our mobility scenarios [18] do not account for additional interventions that may be

implemented, such as mass testing and contact tracing. It is also likely that when interventions are lifted behaviour may

modify the effect sizes of mobility and reduce the impact of mobility on transmission. Factors such as increased use of

masks and increased adherence to social distancing are examples. Given these factors we caution the reader to look at

our scenarios as pessimistic, but illustrative of the potential risks.

We define scenarios based on percent return to baseline mobility, which is by definition 0. As an example, say that

currently mobility is 50% lower than baseline, or -50%, perhaps due to the introduction of social-distancing NPIs. Then, a

20% increase of mobility from its current level is−50%∗(1−20%) = −40%. Similarly, if mobility in residences increased

by 10% following a stay-at-home order, our 20% scenario reduces this to an 8% increase over baseline. This assumes that

people have begun to resume pre-lockdown behaviour, but have not yet returned to baseline mobility. We hold this 20%

return to baseline constant for the duration of the 8-week scenario.

We present three scenarios (a) constant mobility (mobility remains at current levels for 8 weeks), (b) 20% return to pre-

stay-at-homemobility from current levels and (c) 40% return to pre-stay-at-homemobility from current levels. We justify


https://doi.org/10.25561/79231


TOLA South Atlantic

Mountain Great Lakes Southern Appalachia

Pacific Great Plains Northeast Corridor

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# new infections [95% CI] # new infections [50% CI] # current infections [95% CI] # current infections [50% CI]

Figure 7: Estimates for the effective number of infectious individuals on a day in purple (light purple, 95% CI, dark purple

50% CI) and for newly infected people per day in blue (light blue, 95% CI, dark blue: 50% CI).


https://doi.org/10.25561/79231


Table 2: Posterior model estimates of the number of currently infectious individuals as of 17 May 2020.

State Number of infectious

individuals (mean [95%

credible interval])

State Number of infectious

individuals (mean [95%

credible interval])

Alabama 15,000 [4,000-37,000] Montana 0 [0-1,000]

Alaska 0 [0-2,000] Nebraska 3,000 [0-10,000]

Arizona 40,000 [12,000-93,000] Nevada 5,000 [0-14,000]

Arkansas 1,000 [0-4,000] New Hampshire 4,000 [0-12,000]

California 92,000 [26,000-228,000] New Jersey 94,000 [26,000-227,000]

Colorado 47,000 [15,000-110,000] New Mexico 10,000 [2,000-24,000]

Connecticut 40,000 [11,000-93,000] New York 84,000 [13,000-246,000]

Delaware 9,000 [2,000-22,000] North Carolina 14,000 [3,000-35,000]

District of Columbia 7,000 [1,000-18,000] North Dakota 0 [0-2,000]

Florida 39,000 [10,000-95,000] Ohio 54,000 [17,000-125,000]

Georgia 28,000 [6,000-72,000] Oklahoma 1,000 [0-5,000]

Hawaii 0 [0-1,000] Oregon 1,000 [0-4,000]

Idaho 0 [0-1,000] Pennsylvania 96,000 [23,000-251,000]

Illinois 176,000 [54,000-395,000] Rhode Island 6,000 [1,000-16,000]

Indiana 52,000 [12,000-134,000] South Carolina 7,000 [1,000-19,000]

Iowa 18,000 [5,000-41,000] South Dakota 1,000 [0-5,000]

Kansas 1,000 [0-4,000] Tennessee 6,000 [1,000-17,000]

Kentucky 2,000 [0-7,000] Texas 90,000 [27,000-218,000]

Louisiana 29,000 [6,000-75,000] Utah 1,000 [0-5,000]

Maine 0 [0-1,000] Vermont 0 [0-1,000]

Maryland 37,000 [9,000-91,000] Virginia 27,000 [6,000-66,000]

Massachusetts 96,000 [27,000-232,000] Washington 9,000 [1,000-26,000]

Michigan 21,000 [4,000-59,000] West Virginia 0 [0-1,000]

Minnesota 36,000 [10,000-88,000] Wisconsin 7,000 [1,000-22,000]

Mississippi 22,000 [6,000-51,000] Wyoming 0 [0-1,000]

Missouri 16,000 [4,000-41,000] National 1344000 [368000 -

3320000]


https://doi.org/10.25561/79231


Constant mobility Increased mobility 20% Increased mobility 40%W

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Figure 8: State-level scenario estimates of deaths for Washington, New York, Massachusetts, Florida and California. The

ribbon shows the 95% credible intervals (CIs) for each scenario. The first column of plots show the results of scenario

(a) where mobility is kept constant at pre-stay-at-home levels, the middle column shows results for scenario (b) where

there is a 20% return to pre-epidemic mobility, and the right column shows scenario (c) where there is a 40% return to

pre-epidemic mobility.

the selection of these scenarios by examining how mobility has changed in states that have already begun to relax social

distancing guidelines. For example, Colorado’s stay-at-home order expired on the 26th of April, and activity level reported

by the Colorado Department of Public Health has recovered approximately 30% of the decrease observed following initial

implementation of NPIs [6]. Figure 8 shows the estimated number of deaths for each scenario in the five states discussed

above: Washington, New York, Massachusetts, Florida, and California. Results for all the states modelled are included in

Appendix F. These estimates are certainly not forecasts and are based on multiple assumptions, but they illustrate the

potential consequences of increasing mobility across the general population: in almost all cases, after 8 weeks, a 40%

return to baseline leads to an epidemic larger than the current wave.


https://doi.org/10.25561/79231


3 Conclusions

In this report we use a Bayesian semi-mechanistic model to investigate the impact of these NPIs via changes in mobility.

Our model uses mobility to predict the rate of transmission, neglecting the potential effect of additional behavioural

changes or interventions such as testing and tracing. While mobility will explain a large amount of the variance in Rt,

there is likely to be substantial residual variation which will be geographically heterogeneous. We attempt to account

for this residual variation through a second order, weekly, autoregressive process. This stochastic process is able to

pick up variation drive by the data but is unable to determine associations or causal mechanisms. Figure 12 shows the

residual variation captured by the autoregressive process, and given these lines are flat for the majority of states, we can

conclude that much of the variation we see in the observed death data can be attributed to mobility. However, there are

states, such as New York, where this residual effect is large which suggests that additional factors have contributed to the

reduction in Rt. We hypothesise these could be behavioural changes but testing this hypothesis will require additional

data.

We find that the starting reproduction number is associated with population density and the chronological date of epi-

demic onset. These two relationships suggest two dimensions which may influence the starting reproduction number

and underscore the variability between states. We are cautious to draw any causal relationships from these associations;

our results highlight that more additional studies of these factors are need at finer spatial scales.

We find that the posterior mean of the current reproduction is above 1 in 9 states, with 95% confidence, and above 1

in 25 states with 50% confidence. These current reproduction numbers suggest that in many states the US epidemic is

not under control and caution must be taken in loosening current interventions without additional measures in place.

The high reproduction numbers are geographically clustered in the southern US and Great Plains region, while lower

reproduction numbers are observed in areas that have suffered high COVID-19mortality (such as the Northeast Corridor).

We simulate forwards in time a partial return of mobility back to pre-COVID levels, while keeping all else constant, and

find substantial resurgence is expected. In the majority of states, the deaths expected over a two-month period would

exceed current levels bymore than two-fold. This increase in mobility is modest and held constant for 8 weeks. However,

these results must be heavily caveated: our results do not account for additional interventions that may be introduced

such as mass testing, contact tracing and changing work place/transit practices. Our results also do not account for

behavioural changes that may occur such as increased mask wearing or changes in age specific movement. Therefore,

our scenarios are pessimistic in nature and should be interpreted as such. Given these caveats, we conjecture at the

present time that, in the absence of additional interventions (such as mass testing), additional behavioural modifications

are unlikely to substantially reduceRt in of their own.

We estimate the number of individuals that have been infected by SARS-CoV2 to date. Our attack rates are sensitive to

the assumed values of infection fatality rate (IFR). We account for each individual state’s age structure, and further adjust

for contact mixing patterns [19]. To ensure assumptions about IFR do not have undue influence on our conclusions, we

incorporate prior noise in the estimate, and performa sensitivity analysis using different contactmatrices. Also, our attack

rates for New York are in line with those from recent serological studies [1]. We show that while reductions in the daily

infections continue, the reservoir of infectious individuals remains large. This reservoir also implies that interventions

should remain in place longer than the daily case count implies, as trends in the number of infectious individuals lags

behind. Themagnitude of difference between newly infected and currently infected individuals suggest thatmass testing


https://doi.org/10.25561/79231


and isolation could be an effective intervention.

Our results suggest that while the US has substantially reduced its reproduction numbers in all states, there is little

evidence that the epidemic is under control in themajority of states. Without changes in behaviour that result in reduced

transmission, or interventions such as increased testing that limit transmission, new infections of COVID-19 are likely to

persist, and, in the majority of states, grow.

4 Data

Our model uses daily real-time state-level aggregated data published by New York Times (NYT) [20] for New York State

and John Hopkins University (JHU) [3] for the remaining states. There is no single source of consistent and reliable data

for all 50 states. We acknowledge that data issues such as under reporting and time lags can influence our results. In

previous reports [8, 9, 7] we have shown our modelling methodology is generally robust to these data issues due to

pooling. However, we do recognise no modelling methodology will be able to surmount all data issues; therefore these

results should be interpreted as the best estimates based on current data, and are subject to change with future data

consolidation. JHU andNYT provide information on confirmed cases and deaths attributable to COVID-19, however again,

the case data are highly unrepresentative of the incidence of infections due to under-reporting and systematic and state-

specific changes in testing. We, therefore, use only deaths attributable to COVID-19 in our model. While the observed

deaths still have some degree of unreliability, again due to changes in reporting and testing, we believe the data are of

sufficient fidelity to model. For age specific population counts we use data from the U.S. Census Bureau in 2018 [21]. The

timing of social distancing measures was collated by the University of Washington [11].

We use theGoogleMobility Report [5] 3 which provides data onmovement in theUSA by states and highlights the percent

change in visits to:

• Grocery & pharmacy: Mobility trends for places like grocerymarkets, foodwarehouses, farmersmarkets, speciality

food shops, drug stores, and pharmacies.

• Parks: Mobility trends for places like local parks, national parks, public beaches, marinas, dog parks, plazas, and

public gardens.

• Transit stations: Mobility trends for places like public transport hubs such as subway, bus, and train stations.

• Retail & recreation: Mobility trends for places like restaurants, cafes, shopping centres, theme parks, museums,

libraries, and movie theatres.

• Residential:Mobility trends for places of residence.

• Workplaces: Mobility trends for places of work.

The mobility data show length of stay at different places compared to a baseline. It is therefore relative, i.e. mobility of

-20% means that, compared to normal circumstances individuals are engaging in a given activity 20% less.

3We use mobility data from Google, which was last updated on 9th May 2020. For dates after 9th May 2020, we impute the mobility data with the

median of last seven days.


https://doi.org/10.25561/79231


5 Methods

We introduced a new Bayesian framework for estimating the transmission intensity and attack rate (percentage of the

population that has been infected) of COVID-19 from the reported number of deaths in a previous report [7]4. This frame-

work uses the time-varying reproduction numberRt to inform a latent function for infections, and then these infections,

together with probabilistic lags, are calibrated against observed deaths. Observed deaths, while still susceptible to under

reporting and delays, are more reliable than the reported number of confirmed cases, although the early focus of most

surveillance systems on cases with reported travel histories to China may have missed some early deaths. Changes in

testing strategies during the epidemic mean that the severity of confirmed cases as well as the reporting probabilities

changed in time and may thus have introduced bias in the data.

In this report, we adapt our original Bayesian semi-mechanistic model of the infection cycle to the states in the USA. We

infer plausible upper and lower bounds (Bayesian credible intervals) of the total populations infected (attack rates) and

the reproduction number over time (Rt). In our framework we parametrize Rt as a function of Google mobility data.

We fit the model jointly to COVID-19 data from all regions to assess whether there is evidence that changes in mobility

have so far been successful at reducingRt below 1. Our model is a partial pooling model, where the effect of mobility is

shared, but region- and state-specific modifiers can capture differences and idiosyncrasies among the regions.

We note that future directions should focus on embedding mobility in realistic contact mechanisms to establish a closer

relationship to transmission.

5.1 Model specifics

Weobserve daily deathsDt,m for days t ∈ {1, . . . , n} and statesm ∈ {1, . . . ,M}. These daily deaths aremodelled using

a positive real-valued function dt,m = E[Dt,m] that represents the expected number of deaths attributed to COVID-19.

The daily deathsDt,m are assumed to follow a negative binomial distribution with mean dt,m and variance dt,m +d2t,m

φ ,

where ψ follows a positive half normal distribution, i.e.

Dt,m ∼ Negative Binomial

(dt,m, dt,m +

d2t,mψ

),

ψ ∼ N+(0, 5).

Here, N (µ, σ) denotes a normal distribution with mean µ and standard deviation σ. We say that X follows a positive

half normal distributionN+(0, σ) ifX ∼ |Y |, where Y ∼ N (0, σ).

To mechanistically link our function for deaths to our latent function for infected cases, we use a previously estimated

COVID-19 infection fatality ratio (IFR, probability of death given infection) together with a distribution of times from

infection to death π. Details of this calculation can be found in [22, 23]. From the above, every region has a specific

mean infection fatality ratio ifrm (see Appendix G). To incorporate the uncertainty inherent in this estimate we allow the

4Similar to our previous report [7], we seed each epidemic for 5 consecutive days starting 30 days before the state reached ten cumulative deaths.

Wyoming did not report more than 10 deaths in our data set, so we use a threshold of five instead.


https://doi.org/10.25561/79231


ifrm for every state to have additional noise around the mean. Specifically we assume

ifr∗m ∼ ifrm ·N(1, 0.1).

We believe a large-scale contact survey similar to polymod [19] has not been collated for the USA, so we assume the

contact patterns are similar to those in the UK. We conducted a sensitivity analysis, shown in Appendix G, and found that

the IFR calculated using the contact matrices of other European countries lay within the posterior of ifr∗m.

Using estimated epidemiological information from previous studies [22, 23], we assume the distribution of times from

infection to death π (infection-to-death) to be

π ∼ Gamma(5.1, 0.86) + Gamma(17.8, 0.45).

The expected number of deaths dt,m, on a given day t, for statem is given by the following discrete sum:

dt,m = ifr∗m

t−1∑τ=0

cτ,mπt−τ ,

where cτ,m is the number of new infections on day τ in statem and where π is discretized via πs =∫ s+0.5

s−0.5π(τ)dτ for

s = 2, 3, ..., and π1 =∫ 1.5

0π(τ)dτ , where π(τ) is the density of π.

The true number of infected individuals, c, is modelled using a discrete renewal process. We specify a generation distri-

bution g with density g(τ) as:

g ∼ Gamma(6.5, 0.62).

Given the generation distribution, the number of infections ct,m on a given day t, and statem, is given by the following

discrete convolution function:

ct,m = St,mRt,m

t−1∑τ=0

cτ,mgt−τ , (1)

St,m = 1−∑t−1

i=0 ci,mNm

where, similar to the probability of death function, the generation distribution is discretized by gs =∫ s+0.5

s−0.5g(τ)dτ for

s = 2, 3, ..., and g1 =∫ 1.5

0g(τ)dτ . The population of state m is denoted by Nm . We include the adjustment factor

St,m to account for the number of susceptible individuals left in the population.

We parametriseRt,m as a linear function of the relative change in time spent (from a baseline)

Rt,m = R0,m · f(−(

3∑k=1

Xt,m,kαk)− Yt,mαregion

r(m) − Zt,mαstatem − εm,wm(t)), (2)

where f(x) = 2 exp(x)/(1+ exp(x)) is twice the inverse logit function. Xt,m,k are covariates that have the same effect

for all states, Yt,m is a covariate that also has a region-specific effect, r(m) ∈ {1, . . . , R} is the region a state is in (see

Figure 1), Zt,m is a covariate that has a state-specific effect and εm,wm(t) is a weekly AR(2) process, centred around 0,

that captures variation between states that is not explained by the covariates.

The prior distribution forR0,m[24] was chosen to be

R0,m ∼ N (3.28, κ) with κ ∼ N+(0, 0.5),


https://doi.org/10.25561/79231


where κ is the same among all states.

In the analysis of this paper we chose the following covariates: Xt,m,1 = M averaget,m , Xt,m,2 = M transit

t,m , Xt,m,3 =

M residentialt,m , Yt,m = M average

t,m , and Zt,m = M transitt,m , where the mobility variables are from [5] and defined as follows

(all are encoded so that 0 is the baseline and 1 is a full reduction of the mobility in this dimension):

• M averaget,m is an average of retail and recreation, groceries and pharmacies, and workplaces. An average is taken as

these dimensions are strongly collinear.

• M transitt,m is encoding mobility for public transport hubs. For states where less than 20% of the working population

aged 16 and over uses public transportation, we setM transitt,m = 0, i.e. this mobility has no effect on transmission.

For states in which more than 20% of the working population commutes using public transportation,M transitt,m is the

mobility on transit.

• M residentialt,m are the mobility trends for places of residences.

The weekly, state-specific effect is modelled as a weekly AR(2) process, centred around 0with stationary standard devia-

tion σw that starts on the day after the emergency decree in in a state. Before the emergency decree, there is no random

weekly effect, so ε1,m = 0. Afterwards, the AR(2) process starts with ε2,m ∼ N (0, σ∗w),

εw,m ∼ N (ρ1εw−1,m + ρ2εw−2,m, σ∗w) form = 3, 4, . . . (3)

with independent priors on ρ1 and ρ2 that are normal distributions conditioned to be in [0, 1]; the prior for ρ1 is a

N (0.8, .05) distribution conditioned to be in [0, 1] the prior for ρ2 is a N (0.1, .05) distribution, conditioned to be in

[0, 1]. The prior for σw, the standard deviation of the stationary distribution of εw is chosen as σw ∼ N+(0, .2).

The standard deviation of the weekly updates to achieve this standard deviation of the stationary distribution is σ∗w =

σw√1− ρ21 − ρ22 − 2ρ21ρ2/(1− ρ2).

The conversion from days to weeks is encoded in wm(t). We set wm(t) = 1 for all t ≤ temergencym , which is the day of the

emergency decree in that state. Then, every 7 days, wm is incremented, i.e. wm(t) = bmax(t− temergencym − 1, 0)/7c+ 2

for t > temergencym . Due to the lag between infection and death, our estimates ofRt in the last twoweeks before the end of

our observations are (almost) not informed by corresponding death data. Therefore, we assume that the last two weeks

have the same random weekly effect as the week 3 weeks before the end of observation.

The prior distribution for the shared coefficients were chosen to be

αk ∼ N (0, 0.5), k = 1, . . . , 3,

and the prior distribution for the pooled coefficients were chosen to be

αregionr ∼ N (0, γr), r = 1, . . . , R, with γr ∼ N+(0, 0.5),

αstatem ∼ N (0, γs),m = 1, . . . ,M with γs ∼ N+(0, 0.5).

We assume that seeding of new infections begins 30 days before the day after a state has cumulatively observed 10

deaths. From this date, we seed our model with 6 sequential days of an equal number of infections: c1,m = · · · =


https://doi.org/10.25561/79231


c6,m ∼ Exponential( 1τ ), where τ ∼ Exponential(0.03). These seed infections are inferred in our Bayesian posterior

distribution.

We estimated parameters jointly for all states in a single hierarchical model. Fitting was done in the probabilistic pro-

gramming language Stan[25] using an adaptive Hamiltonian Monte Carlo (HMC) sampler.

6 Acknowledgements

We would like to thank Amazon AWS and Microsoft Azure for computational credits and we would like to thank the

Stan development team for their ongoing assistance. This work was supported by Centre funding from the UK Medical

Research Council under a concordat with the UK Department for International Development, the NIHR Health Protection

Research Unit in Modelling Methodology and Community Jameel.

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A Mobility regression analysis

In Figure 9 we regress NPIs against average mobility. We parameterise NPIs as piece-wise constant functions that are

zero when the intervention has not been implemented and one when it has. We evaluate the correlation between the

predictions from the linear model and the actual averagemobility. We also lag the timing of interventions and investigate

its impact on predicted correlation.


http://www.covid19statepolicy.org

http://www.covid19statepolicy.org

https://data.census.gov/cedsci/

https://morningconsult.com/form/coronavirus-outbreak-tracker/

https://www.vox.com/2015/8/10/9118199/public-transportation-subway-buses

https://www.vox.com/2015/8/10/9118199/public-transportation-subway-buses

https://science.sciencemag.org/content/362/6410/75.full.pdf

https://science.sciencemag.org/content/362/6410/75.full.pdf

https://science.sciencemag.org/content/362/6410/75

https://sf.gov/sites/default/files/2020-04/2020.04.29%20FINAL%20%28signed%29%20Health%20Officer%20Order%20C19-07c-%20Shelter%20in%20Place.pdf

https://sf.gov/sites/default/files/2020-04/2020.04.29%20FINAL%20%28signed%29%20Health%20Officer%20Order%20C19-07c-%20Shelter%20in%20Place.pdf

https://www.nytimes.com/interactive/2020/us/states-reopen-map-coronavirus.html

https://doi.org/10.1371/journal.pmed.0050074

https://github.com/nytimes/covid-19-data

https://github.com/nytimes/covid-19-data

https://censusreporter.org

https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/news--wuhan-coronavirus/

https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/news--wuhan-coronavirus/

http://www.jstatsoft.org/v76/i01/

https://doi.org/10.25561/79231


0

5

10

15

20

0.00 0.25 0.50 0.75 1.00Correlation

Num

ber

of S

tate

s

0.4

0.5

0.6

0.7

0.8

−20 −10 0 10 20Lag

Cor

rela

tion

Figure 9: Mobility regression analysis.

B Effect sizes

●

●

●

●

●

●

●

●

TOLA

Southern Appalachia

South Atlantic

Pacific

Northeast Corridor

Mountain

Great Plains

Great Lakes

−25% 0% 25% 50%Relative % reduction in Rt

Ave

rage

mob

ility

Figure 10: Regional covariate effect size plots.


https://doi.org/10.25561/79231


●

●

●

●

●

●

●

●Washington

New York

New Jersey

Massachusetts

Maryland

Illinos

District of Columbia

California

−25% 0% 25%Relative % reduction in Rt

Tran

sit

Figure 11: State-level covariate effect size plots.

C State-specific weekly effects after emergency decree

Our model includes a state-specific weekly effect εw,m (see equations 2, 3) for every weekw after the emergency decree

of that state. As described in Section 5, We assign an autoregressive process with mean 0 as prior to this effect. This

weekly effect is held constant for the 4 weeks up to the present week. Figure 12 shows the posterior of this effect on the

same scale as in Figure 2, that is, the percent reduction inRt with mobility variables held constant5. Values above 0 have

the interpretation that the state-specific weekly effect lowers the reproduction numberRt,m, i.e. transmission for week

t and statem is lower than what is explained by the mobility covariates.

5Draws from the posterior are transformed with 1− f(−εm,wm(t)), where f(x) = 2 exp(x)/(1 + exp(x)) is twice the inverse logit function.


https://doi.org/10.25561/79231


Hawaii

Texas Louisiana Florida

California Arizona New Mexico Oklahoma Arkansas Mississippi Alabama Georgia South Carolina

Nevada Utah Colorado Kansas Missouri Tennessee Kentucky West Virginia North Carolina Maryland

Oregon Idaho Wyoming Nebraska Iowa Illinois Indiana Ohio Virginia District of Columbia Delaware

Washington Montana North Dakota South Dakota Minnesota Wisconsin Michigan Pennsylvania New Jersey Rhode Island

New York Connecticut Massachusetts

Alaska Vermont New Hampshire Maine

−50%0%

50%

−50%0%

50%

−50%0%

50%

−50%0%

50%

−50%0%

50%

−50%0%

50%

−50%0%

50%

−50%0%

50%

Effe

ct

Figure 12: Percent reduction inRt due to the weekly, state-level autoregressive effect after the emergency decree.


https://doi.org/10.25561/79231


D Model predictions for all states

State-level estimates of infections, deaths and Rt. Left: daily number of deaths, brown bars are reported deaths, blue

bands are predicted deaths, dark blue 50% credible interval (CI), light blue 95% CI. Middle: daily number of infections,

brown bars are reported infections, blue bands are predicted infections, CIs are same as left. The number of daily infec-

tions estimated by our model drops immediately after an intervention, as we assume that all infected people become

immediately less infectious through the intervention. Afterwards, if theRt is above 1, the number of infections will start

growing again. Right: time-varying reproduction numberRt dark green 50%CI, light green 95%CI. Icons are interventions

shown at the time they occurred.

0.00

0.25

0.50

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1.00

10 F

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Credible intervals

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Alabama

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Interventions

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Credible intervals

50%

95%

0

2

4

6

8

10 F

eb

24 F

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9 M

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6 A

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4 M

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18 M

ay

Dai

ly n

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Arkansas

0

100

200

300

400

500

10 F

eb

24 F

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9 M

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23 M

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6 A

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20 A

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4 M

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0

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10 F

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9 M

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6 A

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20 A

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4 M

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Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

50

100

150

10 F

eb

24 F

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9 M

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23 M

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6 A

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20 A

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California

0

10,000

20,000

30,000

10 F

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24 F

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9 M

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23 M

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6 A

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4 M

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5

10 F

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24 F

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9 M

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23 M

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6 A

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Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%


https://doi.org/10.25561/79231


0

50

100

10 F

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24 F

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Colorado

0

5,000

10,000

15,000

20,000

10 F

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24 F

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0

1

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3

4

10 F

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24 F

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9 M

ar

23 M

ar

6 A

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20 A

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Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

50

100

150

200

10 F

eb

24 F

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9 M

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23 M

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6 A

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20 A

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4 M

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18 M

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Dai

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Connecticut

0

5,000

10,000

15,000

20,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

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20 A

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4 M

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Dai

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infe

ctio

ns

0

1

2

3

4

5

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

5

10

15

20

10 F

eb

24 F

eb

9 M

ar

23 M

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6 A

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20 A

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4 M

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18 M

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Dai

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District of Columbia

0

1,000

2,000

3,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

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20 A

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4 M

ay

Dai

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infe

ctio

ns

0

1

2

3

4

5

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

4

8

12

16

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

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20 A

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4 M

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18 M

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Dai

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Delaware

0

1,000

2,000

3,000

4,000

10 F

eb

24 F

eb

9 M

ar

23 M

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ctio

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0

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2

3

4

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

25

50

75

100

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

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4 M

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18 M

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Dai

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Florida

0

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10 F

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Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

25

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75

100

10 F

eb

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Georgia

0

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12,000

10 F

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Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%


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0

0

1

2

2

10 F

eb

24 F

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23 M

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Hawaii

0

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10 F

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0.0

0.5

1.0

1.5

2.0

2.5

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

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4 M

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Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

2

4

6

10 F

eb

24 F

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Idaho

0

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400

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10 F

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0

1

2

3

10 F

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24 F

eb

9 M

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23 M

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Rt

Timing

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Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

50

100

150

200

10 F

eb

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9 M

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Illinois

0

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60,000

90,000

10 F

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Rt

Timing

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Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

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50

100

150

10 F

eb

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Indiana

0

10,000

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30,000

10 F

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Timing

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Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

5

10

15

20

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Iowa

0

2,000

4,000

6,000

8,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

5

10

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Kansas

0

500

1,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%


https://doi.org/10.25561/79231


0

5

10

15

20

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Kentucky

0

500

1,000

1,500

2,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

50

100

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Louisiana

0

5,000

10,000

15,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

5

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

1

2

3

4

5

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Maine

0

100

200

300

400

500

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

25

50

75

100

125

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Maryland

0

5,000

10,000

15,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

5

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

100

200

300

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Massachusetts

0

10,000

20,000

30,000

40,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

2

4

6

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

50

100

150

200

250

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Michigan

0

10,000

20,000

30,000

40,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

5

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%


https://doi.org/10.25561/79231


0

10

20

30

40

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Minnesota

0

5,000

10,000

15,000

20,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

10

20

30

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Mississippi

0

2,500

5,000

7,500

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

20

40

60

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Missouri

0

2,000

4,000

6,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

1

2

3

4

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Montana

0

100

200

300

400

500

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0.0

0.5

1.0

1.5

2.0

2.5

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

5

10

15

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Nebraska

0

400

800

1,200

1,600

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

10

20

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Nevada

0

500

1,000

1,500

2,000

2,500

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%


https://doi.org/10.25561/79231


0

5

10

15

20

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

New Hampshire

0

500

1,000

1,500

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

100

200

300

400

500

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

New Jersey

0

20,000

40,000

60,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

2

4

6

8

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

5

10

15

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

New Mexico

0

1,000

2,000

3,000

4,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

300

600

900

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

New York

0

50,000

100,000

150,000

200,000

250,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0.0

2.5

5.0

7.5

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

10

20

30

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

North Carolina

0

2,000

4,000

6,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

2

4

6

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

North Dakota

0

100

200

300

400

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%


https://doi.org/10.25561/79231


0

50

100

150

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Ohio

0

5,000

10,000

15,000

20,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

5

10

15

20

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Oklahoma

0

500

1,000

1,500

2,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

3

6

9

12

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Oregon

0

250

500

750

1,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

100

200

300

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Pennsylvania

0

10,000

20,000

30,000

40,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

5

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

10

20

30

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Rhode Island

0

1,000

2,000

3,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

10

20

30

40

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

South Carolina

0

1,000

2,000

3,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%


https://doi.org/10.25561/79231


0

1

2

3

4

5

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

South Dakota

0

100

200

300

400

500

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

4

8

12

16

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Tennessee

0

1,000

2,000

3,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

20

40

60

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Texas

0

20,000

40,000

60,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

5

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

2

4

6

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Utah

0

250

500

750

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

1

2

3

4

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Vermont

0

100

200

300

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

20

40

60

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Virginia

0

3,000

6,000

9,000

12,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

5

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%


https://doi.org/10.25561/79231


0

10

20

30

40

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Washington

0

1,000

2,000

3,000

4,000

5,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

2

4

6

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

West Virginia

0

100

200

300

400

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

5

10

15

20

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Wisconsin

0

1,000

2,000

3,000

4,000

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0

1

2

3

4

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

0

1

2

3

4

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

18 M

ay

Dai

ly n

umbe

r of

dea

ths

Wyoming

0

100

200

300

400

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Dai

ly n

umbe

r of

infe

ctio

ns

0.0

0.5

1.0

1.5

2.0

2.5

10 F

eb

24 F

eb

9 M

ar

23 M

ar

6 A

pr

20 A

pr

4 M

ay

Rt

Timing

Started

Eased

Interventions

Emergency decree


Business closure

Restaurant closure

School closure


Credible intervals

50%

95%

E Effective number of infectious individuals for all states

The effective number of infectious individuals, c∗, on a given day is calculated by weighing how infectious a previously

infected individual is on a given day. The fully infectious average includes asymptotic and symptomatic individuals. Esti-

mates of the effective number of infectious individuals for all states can be found in Figure 13.

To bemore precise, the effective number of infectious individuals of infectious individuals, c∗, is calculated by first rescal-

ing the generation distribution by its maximum, i.e. g∗τ = gτmaxt gt

. Based on (1), the number of infectious individuals is

then calculated from the number of previously infected individuals, c, using the following:

c∗t,m =

t−1∑τ=0

cτ,mg∗t−τ ,

where ct,m is the number of new infections on day t in statem. A plot of g∗τ can be found in Figure 14.


https://doi.org/10.25561/79231


Hawaii

Texas Louisiana Florida

California Arizona New Mexico Oklahoma Arkansas Mississippi Alabama Georgia South Carolina

Nevada Utah Colorado Kansas Missouri Tennessee Kentucky West Virginia North Carolina Maryland

Oregon Idaho Wyoming Nebraska Iowa Illinois Indiana Ohio Virginia District of Columbia Delaware

Washington Montana North Dakota South Dakota Minnesota Wisconsin Michigan Pennsylvania New Jersey Rhode Island

New York Connecticut Massachusetts

Alaska Vermont New Hampshire Maine

24 F

eb

23 M

ar

20 A

pr

18 M

ay

24 F

eb

23 M

ar

20 A

pr

18 M

ay

24 F

eb

23 M

ar

20 A

pr

18 M

ay

24 F

eb

23 M

ar

20 A

pr

18 M

ay

24 F

eb

23 M

ar

20 A

pr

18 M

ay

24 F

eb

23 M

ar

20 A

pr

18 M

ay

24 F

eb

23 M

ar

20 A

pr

18 M

ay

24 F

eb

23 M

ar

20 A

pr

18 M

ay

24 F

eb

23 M

ar

20 A

pr

18 M

ay

24 F

eb

23 M

ar

20 A

pr

18 M

ay

24 F

eb

23 M

ar

20 A

pr

18 M

ay

24 F

eb

23 M

ar

20 A

pr

18 M

ay0

1,000

2,000

3,000

0

2,500

5,000

7,500

10,000

12,500

0

50,000

100,000

150,000

200,000

250,000

0

5,000

10,000

15,000

20,000

0

5,000

10,000

15,000

20,000

0

500

1,000

1,500

2,000

2,500

0

50,000

100,000

150,000

0

100,000

200,000

300,000

400,000

0

5,000

10,000

15,000

20,000

0

25,000

50,000

75,000

100,000

0

500,000

1,000,000

1,500,000

0

100,000

200,000

0

20,000

40,000

60,000

0

10,000

20,000

30,000

0

5,000

10,000

15,000

20,000

0

25,000

50,000

75,000

100,000

0

50,000

100,000

0

1,000

2,000

3,000

0

20,000

40,000

60,000

0

50,000

100,000

150,000

200,000

250,000

0

50,000

100,000

0

5,000

10,000

0

10,000

20,000

30,000

0

5,000

10,000

15,000

20,000

0

100,000

200,000

300,000

400,000

0

5,000

10,000

15,000

0

10,000

20,000

30,000

40,000

50,000

0

25,000

50,000

75,000

0

10,000

20,000

30,000

40,000

0

10,000

20,000

30,000

40,000

0

1,000

2,000

3,000

4,000

0

25,000

50,000

75,000

100,000

125,000

0

1,000

2,000

3,000

4,000

0

2,500

5,000

7,500

10,000

0

2,500

5,000

7,500

0

4,000

8,000

12,000

0

50,000

100,000

150,000

200,000

0

1,000

2,000

0

500

1,000

1,500

2,000

0

30,000

60,000

90,000

120,000

0

5,000

10,000

15,000

20,000

25,000

0

1,000

2,000

0

1,000

2,000

3,000

0

1,000

2,000

3,000

4,000

5,000

0

25,000

50,000

75,000

100,000

0

500

1,000

1,500

2,000

0

10,000

20,000

30,000

40,000

0

2,000

4,000

6,000

0

4,000

8,000

12,000

16,000

0

50,000

100,000

150,000

200,000

250,000

0

500

1,000

1,500

2,000

2,500

Tota

l num

ber

of in

fect

ious

peo

ple

Figure 13: Estimates for the effective number of infectious individuals over time. The light purple region shows the 95%

credible intervals and the dark purple region shows the 50% credible intervals.

●

●

●

● ●

●

●

●

●

●

●

●

●

●●

●●

● ● ●

0 5 10 15 20

0.0

0.2

0.4

0.6

0.8

1.0

nubmer of days τ since infection

infe

ctio

usne

ss g

τ*

Figure 14: Infectiousness g∗τ of an infected individual over time.

F Scenario results for all states

We show here state level scenario plots of an increase of mobility 20% and 40% of current levels.


https://doi.org/10.25561/79231


HI

TX LA FL

CA AZ NM OK AR MS AL GA SC

NV UT CO KS MO TN KY WV NC MD

OR ID WY NE IA IL IN OH VA DC DE

WA MT ND SD MN WI MI PA NJ RI

NY CT MA

AK VT NH ME

1 M

ar

1 A

pr

1 M

ay

1 Ju

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Jul

1 M

ar

1 A

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1 M

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1 Ju

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1 M

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1 A

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1 M

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1 Ju

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Jul

1 M

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1 A

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1 M

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1 Ju

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Jul

1 M

ar

1 A

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1 M

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1 Ju

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1 M

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1 A

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1 M

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1 Ju

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1 M

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1 A

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1 M

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1 Ju

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1 M

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1 A

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1 M

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1 Ju

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1 M

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1 A

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1 M

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1 Ju

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1 M

ar

1 A

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1 M

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1 Ju

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Jul

1 M

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1 M

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1 Ju

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1 M

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1 A

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1 M

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1 Ju

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Jul

012345

050

100150200

0500

1,0001,500

0

50

100

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01234

0100200300

0250500750

1,0001,250

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20

40

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0250500750

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1,0001,5002,000

0

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1,000

1,500

0250500750

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01,0002,0003,0004,000

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1,0001,5002,0002,500

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0100200300400

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0100200300

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01,0002,0003,0004,0005,000

00122

Dai

ly n

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dea

ths

Scenarios Increased mobility 40% Increased mobility 20% Constant mobility

Figure 15: State-level scenario estimates for deaths. The blue ribbon shows the 95% credible intervals (CIs) for scenario

(a) where mobility is kept constant at pre-lock down levels, the yellow ribbon shows the same CIs for scenario (b) where

there is a 20% return to pre-epidemic mobility and scenario (c) where there is a 40% return to pre-epidemic.

G Sensitivity analysis to infection fatality ratio

Geographic-specific contact surveys are important for calculating theweighted IFR values according to themethods in [22,

23]. There is no large-scale cross-generational contact survey, similar to the polymod survey [19], implemented in the

USA. Therefore, it was important to understand if the model was robust to changes in the underlying contact survey.

We calculated the IFRs using three different contact matrices: UK, France and Netherlands. We believe that the USA is

culturally closest to that UK out of those countries we had contact matrices for, but also considered France where we

saw the greatest mixing of the elderly and the Netherlands which showed the average behaviour of the European studies

used in [23]. We found that the IFR, calculated for each state using the three contact matrices, lay within the posterior

of IFR in our model (Figure 16). We also noted that our results remained approximately constant when using the IFR

calculated from the three different contact matrices as the mean of the prior IFR in out model, see Section 5.

Since we are using the same contact matrix across all the states, the differences in IFR are due to the population de-

mographics and not due to differential contacts. The low IFR in Texas and Utah reflects the younger population there

whereas the higher IFR in Florida and Maine is due to the older population. This is a limitation of our methods.


https://doi.org/10.25561/79231


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●WyomingWisconsin

West VirginiaWashington

VirginiaVermont

UtahTexas

TennesseeSouth Dakota

South CarolinaRhode IslandPennsylvania

OregonOklahoma

OhioNorth Dakota

North CarolinaNew York

New MexicoNew Jersey

New HampshireNevada

NebraskaMontanaMissouri

MississippiMinnesota

MichiganMassachusetts

MarylandMaine

LouisianaKentucky

KansasIowa

IndianaIllinoisIdaho

HawaiiGeorgiaFlorida

District of ColumbiaDelaware

ConnecticutColoradoCaliforniaArkansas

ArizonaAlaska

Alabama

0.006 0.008 0.010 0.012ifr

Sta

te

●

●

●

●

France

Netherlands

UK

Posterior

Figure 16: Sensitivity analysis for IFR. The red, green and blue dots show the IFR values calculated according to [22, 23]

using the French, Dutch and and UK contact matrices respectively. The purple dot shows the mean of our posterior

estimates for the IFR run using the UK contact matrix estimate and the purple error shows the 95% credible intervals of

the distribution.


https://doi.org/10.25561/79231